A two-dimensional, two-state model is used to model the UV-laser-induced photodesorption dynamics of NH3 and ND3 from Cu(111) by solving the nuclear time-dependent Schrodinger equation. By projecting the asymptotic wave functions on the asymptotic ("umbrella") eigenstates of NH3/ND3, we find that the molecules leave the surface vibrationally hot, in agreement with experimental data. Within individual asymptotic tunneling doublets, however, the desorbates are clearly non-Boltzmann with molecules of "gerade" symmetry desorbing with increased probability. Our study correlates this parity selection with details of the electronic ground state potential energy surface. An experimentally observed strong isotope effect in the desorption yields for the different isotopomers is traced back mainly to differences between the vibrational frequencies of the "umbrella" mode, in accord with earlier, classical models. Additionally, small tunneling and moderate zero-point contributions are observed. Finally, the possibility of bend and isotope selective photochemistry at surfaces, based on a two-photon IR+UV strategy is demonstrated.